System and method for creating a poker algorithm capable of independently playing and training users how to play consistently optimal poker

ABSTRACT

An original system and method for solving the card game known as Texas Hold&#39;em Poker is disclosed. Mathematical calculations as well as game theory tactics are utilized to determine the optimal strategy for any possible situation that could potentially arise in Texas Hold&#39;em Poker, as well as other variations of poker where the methodology also applies. One embodiment of the invention involves a fully automated electronic poker simulator that would allow the user to play a complete and genuine game of electronic poker against any number of computerized or live opponents, while simultaneously utilizing features of the poker simulator to learn how to play consistently optimal poker. Another embodiment would be to utilize the unique and specific methodology described herein to develop an artificially intelligent poker algorithm that can independently play consistently optimal poker in any possible scenario.

CROSS REFERENCE TO RELATED APPLICATIONS

Provisional Patent Application #152865989 filed on Jun. 25, 2019

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable

REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTINGCOMPACT DISC APPENDIX

Not Applicable

FIELD OF THE INVENTION

The invention's field relates to a system and method for developing anoptimal strategy for playing various forms of Poker, utilizing a widerange of mathematical calculations and game theory tactics.

BACKGROUND OF THE INVENTION

The game of Poker, and Texas Hold'em Poker in particular, has gainedtremendous popularity in recent decades. Part of the appeal of the gameis the combination of both luck and skill that is required to win. Inthe short run, luck is the primary factor that determines who wins andwho loses each hand. However, players with superior strategy and skillswill win in the long run. This has driven many professional andrecreational poker players to seek out effective methods of improvingtheir poker skills.

Various training methods aimed at improving user poker skills are widelyavailable. Countless books and online tutorials exist with an array ofvarying poker strategies and guidelines. There are also a number ofproprietary poker training methods that have been granted patents inrecent years. The closest published patent application to the currentinvention is Patent # U.S. Pat. No. 8,152,618 B1 (Advancements inComputerized Poker Training and Analysis, Blay et al). This prior artapplication is primarily limited as follows:

1. The method and system disclosed can generally only be applied to apre-determined field of potential poker scenarios. This limitationinhibits users from being able to play a complete game of genuine pokerwhile they learn the optimal poker decision making process.

2. The method and system disclosed is often dependent on poker strategyadvice from human professionals. As such, the process is not fullyautomated and provides little certainty regarding the accuracy of saidprofessional advice.

There have also been various computerized Texas Hold'em Poker algorithmscreated in recent years. These algorithms primarily utilize some form ofCounterfactual Regret Minimization in which the algorithm learns frommillions of iterations of playing poker against itself in order to learnthe optimal decisions in every possible scenario.

However, due to the high degree of complexity inherent to optimal TexasHold'em Poker strategy (particularly multiplayer No Limit Hold'em), todate no one has been capable of developing a fully automated algorithmthat can play and train users in playing consistently optimal TexasHold'em Poker in any possible scenarios, and against any number ofopponents. While there are various Poker training softwares currentlyavailable, none of these softwares allow a user to play a complete gameof genuine no limit hold'em poker against any number of opponents duringa fully automated training process.

Furthermore, the existing poker algorithms that utilize CounterfactualRegret Minimization involve highly complex mathematical calculationsthat inhibit everyday individuals from being capable of performing theprocesses involved. Whereas the methodology presented herein is simpleenough that everyday individuals (with proper training) would be capableof learning how to play consistently optimal Texas Hold'em Poker in anypossible scenarios. Therefore, this invention is a significantimprovement upon the existing art in this field.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1B describe the 169 unique Texas Hold'em starting hands andranks each hand in order of strength.

FIGS. 2A-2B describe the Basic Optimal Strategy fora player's initialpreflop decision to raise/call/fold assuming 0 opponents havevoluntarily entered the hand. FIGS. 2A-2B also describe the ExpectedFrequencies of various initial raise/call/fold decisions when 0opponents have voluntarily entered the hand.

FIGS. 3A-3C describe the Basic Optimal Strategy for a player's initialpreflop decision to raise/call/fold after 1 or more opponents call thebig blind. FIGS. 3A-3C also describe the Expected Frequencies of variousinitial raise/call/fold decisions when facing 1 or more opponent calls.

FIGS. 4A-4I describe the Basic Optimal Strategy for a player's initialpreflop decision to raise/call/fold after 1 opponent has made a potsized raise. FIGS. 4A-4I also describe the Expected Frequencies of allpossible initial raise/call/fold decisions when facing an opponentraise.

FIGS. 5A-5C describe the process for calculating a particular hand'sWeighted Average Equity against an opponent's Estimated Hand Range.

FIGS. 6A-6B describe the Basic Optimal Strategy for a player's decisionto raise/call/fold after an opponent 3-Bet.

FIG. 7 describes 3 general categories of opponents.

FIG. 8 describes various detailed categories of opponents.

FIGS. 9A-9F describe various Adjustments to the Basic Optimal Strategythat are required in order to play consistently optimal Texas Hold'emPoker.

FIGS. 10A-10B describe various postflop examples of hands with WeightedAverage Equity ranging from 0-100%

FIG. 11 describes the Basic Optimal Strategy default bet/raise sizes

FIGS. 12A-12Q provide a detailed outline of the Basic Optimal Strategyfor a Player's initial decision after the flop, and other postflopdecisions.

FIGS. 13A-13C describe the process for revising an opponent estimatedhand range based on opponent decisions, and determining updated opponenthand likelihood weightings.

FIG. 14 describes various features of one embodiment of the inventioninvolving a Poker Simulator/Trainer.

DETAILED DESCRIPTION OF THE INVENTION

Described herein is a unique system and method for solving the variousforms of Texas Hold'em Poker, and developing an optimal strategy thatcan be applied to any possible situation that could potentially arisewhile playing any variation of Texas Hold'em Poker and against anynumber of opponents. The most complex form of Texas Hold'em Poker is NoLimit at a full table (generally 9 or 10 players total). Therefore thissummary will focus on No limit Texas Hold'em at a full table. However,this same methodology can be applied to various other forms of Pokerthat include but are not limited to Limit Hold'em, Short Deck, andOmaha. The same methodology also applies against any number ofopponents.

In Texas Hold'Em there are 169 unique starting hands that a player canbe dealt (without distinguishing between different suits). The optimaldecisions (raise/call/fold or check/bet) are determined based ondetailed statistical calculations and game theory considerations. FIGS.1A-1B rank all 169 unique Texas Hold'em starting hands in order ofstrength. This hand strength ranking will be used to determine aspecific Basic Optimal Strategy in any possible situation. FIGS. 1A-1Bare based on effective stack sizes of around 100 big blinds.

FIGS. 2A-2B describe the Basic Optimal Strategy for a player's initialpreflop decision to raise/call/fold, assuming 0 opponents havevoluntarily entered the hand. FIGS. 2A-2B also describe the ExpectedFrequencies of various initial raise/call/fold decisions when the playeris the initial bettor.

To avoid giving away the strength of any hand, all preflop raises shouldhave a default sizing relative to the pot size. Assuming players haveeffective stack sizes around 100 big blinds, all preflop raises shouldbe pot sized bets (initial raise size=3.5 big blinds). Shorter stacksizes may require smaller than pot raise sizing. Deeper stack sizes mayrequire larger than pot raise sizing.

The next step is to determine how to handle opponent raises/calls. Thisis where Opponent Analysis (information gathered by observing opponentbehavior) becomes crucial to making maximally optimal decisions.Assuming it is the first hand of play and there is no Opponent Analysisavailable, FIGS. 3A-3C outline the Basic Optimal Strategy for a player'sinitial preflop decision to raise/call/fold after 1 or more opponentshave called the big blind. FIGS. 3A-3C also describe the ExpectedFrequencies of various initial raise/call/fold decisions in hands where1 or more opponents have called the big blind.

Similarly, FIGS. 4A-4I describe the Basic Optimal Strategy for aplayer's initial preflop decision to raise/call/fold, after 1 Opponenthas made a pot size raise. FIGS. 4A-4I also describe the ExpectedFrequencies of various initial raise/call/fold decisions in hands where1 opponent has raised.

As specified in FIGS. 2A-2B, 3A-3C, and 4A-4I, there is a range of handswhere Basic Optimal Strategy advises a particular preflop decision(fold/call/raise). Below are 3 examples that will help illustrate how toutilize the data from FIGS. 1A-4I to determine an opponent's EstimatedHand Range in a given situation:

-   -   1. Player is on the button (2 opponents behind) and all        opponents fold to Player. Basic Optimal Strategy would be for        Player to raise with all hands ranging from AA (Hand 1) down to        78o (Hand 72). Therefore, if Player raises, then Player's        Estimated Hand Range=1 to 72.    -   2. Player raises with 8 opponents behind (no limpers), and        opponent calls from the button. Player's Estimated Hand Range=1        to 18, and opponent's Estimated Hand Range=8 to 30.    -   3. Player raises with 8 opponents behind (no limpers), and        opponent 3-bets from the button. Opponent's Estimated<Hand        Range=1 to 7.

Once a player has determined an opponent's Estimated Hand Range in aparticular situation, a player can also determine their own hand'sWeighted Average Equity against the opponent Estimated Hand Range. FIGS.5A-5C provide a detailed example of how to calculate a hand's WeightedAverage Equity against an opponent Estimated Hand Range.

A hand's Weighted Average Equity is revised after almost every opponentdecision, and will be the primary factor in determining the BasicOptimal Strategy throughout all postflop decisions. A player can alsodetermine their own estimated hand range's Weighted Average Equityagainst each hand within an opponent's Estimated Hand Range (player'srange vs opponent's range).

The next step is to determine the Basic Optimal Strategy against anopponent 3-bet (or 4-bet etc.). The Basic Optimal Strategy for dealingwith opponent re-raises is reliant on determining an accurate opponentEstimated Hand Range for any possible situation, then utilizing thatEstimated Hand Range to calculate the payer's Weighted Average Equity(as per FIGS. 5A-5C). FIGS. 6A-6B provide a detailed description for howto utilize Weighted Average Equity to determine the optimal strategy fora player's response to an opponent 3-bet.

The following are 2 additional examples that illustrate the BasicOptimal Strategy decision making process when facing an opponent 3-bet:

-   -   1. All opponents fold to the button, who raises with Ace of        hearts and Ace of diamonds. The small blind folds, then the big        blind 3-bets (pot size raise). The big blind's Estimated Hand        Range=1 to 21. So the button's Weighted Average Equity can be        calculated as follows:

Big Blind Possible Button Equity Estimated Hands Combinations with AA AA1 50% KK 6 82% AKs 2 88% QQ 6 81% JJ 6 81% AKo 6 93% AQs 2 87% 1010 681% AQo 6 93% KQs 4 83% AJs 2 87% 99 6 81% KJs 4 82% QJs 4 81% A10s 287% 88 6 81% KQo 12 87% AJo 6 92% J10s 4 79% Q10s 4 80% K10s 4 82% Total99 85%

-   -   99 total hand combinations within opponent Estimated Hand Range    -   Button has Weighted Average Equity˜85%    -   Because 85% is greater than the 65% 4-bet with position        threshold, the Basic Optimal Strategy would be for Button to        make a pot size 4-bet.    -   2. Player has 8 opponents behind (no limpers) and raises with        Queen of hearts and Queen of diamonds. Opponent with 7 opponents        behind 3-bets, and all other opponents fold. Opponent's        Estimated Hand Range=1 to 6. Player's Weighted Average Equity        can be calculated as follows:

Opponent Possible Estimated Hands Combinations Player Equity AA 6 19% KK6 18% AKs 4 54% QQ 1 50% JJ 6 82% AKo 12 56% Total 35 47%

-   -   35 total hand combinations within standard opponent Estimated        Hand Range    -   Player has Weighted Average Equity˜47%    -   Because 47% is greater than 36% but less than 63%, Basic Optimal        Strategy would be for Player to call the opponent 3-Bet.

The Basic Optimal Strategy described thus far is optimal only if playingagainst opponents that are also playing according to the same BasicOptimal Strategy. However, many opponents do not play according to theBasic Optimal Strategy. Therefore, playing consistently optimal TexasHold'em Poker requires numerous adjustments to the Basic OptimalStrategy based on a wide range of factors.

First and foremost, Opponent Analysis allows a player to categorize eachopponent's playing style in order to determine when to adjust the BasicOptimal Strategy against that particular opponent. This is thefundamental principle of Exploitative poker strategy. FIG. 7 describesthe 3 general categories of opponents: Loose, Optimal, and Tight.

All opponents are initially considered optimal. That is why the BasicOptimal Strategy applies to all hands when there is no hand history withan opponent. Over the course of play, through attentive observation ofevery opponent decision that takes place within each hand, optimalplayers categorize each opponent's decisions as either loose, optimal,or tight in various situations.

Based on the Expected Frequencies calculated in FIGS. 2A-2B, 3A-3C, 4A,4I and 6A-6B, a player is able to gather data on opponentraise/call/fold frequencies as compared to the Expected Frequencies.Opponents that consistently raise/call/fold more (or less) often thanBasic Optimal Strategy expectations are categorized accordingly. Thoseopponents' Estimated Hand Ranges will be adjusted based on theirtendencies. And the Basic Optimal Strategy when playing against thoseopponents would be adjusted accordingly.

In addition to analyzing each opponent's betting statistics, optimalplayers must also analyze each opponent's playing style based on theopponent's cards that are exposed. When opponent cards are exposed atthe completion of a hand, optimal players must count and categorize eachmistake an opponent made during that hand. Opponent mistakes areconsidered significant deviations from the Basic Optimal Strategy,taking all adjustments into account. Keeping track and categorizing allopponent mistakes can be used in combination with each opponent'sfold/call/raise statistics in order to determine how to best categorizeeach opponent. This method of Opponent Analysis will allow optimalplayers to determine how often and to what extent to adjust the BasicOptimal Strategy against each particular opponent. This is accomplishedby further categorizing all non Basic Optimal Strategy opponents intothe Detailed Opponent Categories described in FIG. 8.

In addition to Opponent Analysis, there are numerous additional“Adjustments” to the Basic Optimal Strategy that are required in orderto play consistently optimal Texas Hold'em Poker. FIGS. 9A-9F describesmany of these adjustments in detail, although additional adjustments mayalso be required. Each of the adjustments hated in FIGS. 9A-9F willaffect the Basic Optimal Strategy decisions in various ways.

The final step to playing consistently optimal Texas Hold'em Poker is todetermine how to play the seemingly infinite possible hand scenariosthat can arise on the flop, turn, and river. The primary factor thatdetermines all postflop decisions is a players Weighted Average Equity.FIGS. 10A-10B provide a general outline and examples of flop handstrength tiers, based on a hand's Weighted Average Equity againstopponent Estimated Hand Ranges on the flop.

Basic Optimal Strategy bet/raise sizing on the flop should remainstandard as a percentage of the pot size (similar to preflop raisesizing). The default bet/raise on the flop is ⅔ the pot size. Shortstacks may require less than ⅔ pot bet/raise sizing. Deep stacks mayrequire greater than ⅔ pot bet/raise sizing. Modifying the default betsize will also modify the optimal WAE ranges for postflop decisions.

Turn and river bet/raise sizing should ideally have multiple bet sizeoptions. However, using a default bet/raise size of ½ pot on the turn,and 40% pot on the river, can provide nearly optimal results. Thissimplified bet/raise sizing will also make it significantly easier forpeople to learn the Basic Optimal Strategy decision making process. FIG.11 describes the default bet/raise size for each of the 4 rounds ofbetting.

The primary factor that determines all postflop Basic Optimal Strategyis a player's Weighted Average Equity, calculated using an accurateopponent Estimated Hand Range. Secondary factors that also affectpostflop strategy are:

-   -   1. Number of active opponents in the hand    -   2. Who was the last aggressor (who raised/bet vs who        checked/called).    -   3. Position

Each of the Adjustments described in FIGS. 9A-9F are tertiary factorsthat may or may not adjust the postflop Basic Optimal Strategy.

FIGS. 12A-12Q outline the Basic Optimal Strategy strategy for allpossible initial player decisions on the Flop. FIGS. 12A-12Q includedecision trees that cover all possible WAE figures. (0-100%) and allpossible secondary factors (listed above). Minor revisions to the WAEranges from FIGS. 12A-12Q may be required.

Almost every decision an opponent makes during a hand will affect theirEstimated Hand Range. FIGS. 13A-13C provide a more detailed example forthe process of revising an opponent Estimated Hand Range. The opponent'srevised Estimated Hand Range with likelihood weightings from FIGS.13A-13C would be used to calculate the player's revised Weighted AverageEquity on the Turn (4th community card). A similar process would applyon the River (fifth and final community card).

The methodology described herein can be applied to any possiblesituation that could potentially arise while playing any variation ofTexas Hold'em Poker and against any number of opponents. Resulting in afully automated computer algorithm that can play consistently optimalPoker in all possible scenarios. The algorithm contains elements ofartificial intelligence in that it analyzes opponent decisions and makesadjustments to its strategy based on that analysis. The algorithm couldalso be programmed to play loose, tight, or various other player styles.

One embodiment of the invention involves the use of an electronic “PokerTrainer” that would allow the user to play a complete and genuine gameof electronic poker against a computer and/or other live individuals,and to simultaneously utilize the features of the Poker Trainer to learnhow to play consistently optimal poker. The Poker Trainer would displaythe various statistics and strategies presented herein in an easy toread manner while users are playing real poker against the computerand/or against other live players. This would allow users to learn howto play consistently optimal poker according to the detailed methodologypresented during play. Some of the Poker Trainer's salient features aredescribed in FIG. 14.

Another embodiment of the invention would be to utilize the unique andspecific methodology presented herein to develop an artificiallyintelligent poker algorithm that is capable of independently playingconsistently optimal poker against any number of opponents. Thealgorithm would be programmed to initially play according to the BasicOptimal Strategy. And the algorithm would be programmed to adjust theBasic Optimal Strategy based on Opponent Analysis and the various otherBasic Optimal Strategy Adjustments from FIGS. 9A-9F.

An artificially intelligent algorithm that can independently playconsistently optimal Poker has tremendous application potentialthroughout the Poker Industry. Although the description above containsmany specific details, these should not be construed as limiting thescope of the embodiment. But merely as illustrations of some of thepotential applications. The embodiments described above are meant solelyas examples of the potential application, and in no way limit the scopeof application. Thus, the scope of the invention should be construedbroadly as set forth in the claims.

I claim:
 1. A non-transient computer readable medium comprising programinstructions for causing a computer to perform a method of: obtainingcommunity card poker game data, the community card poker game datacomprising estimated opponent hand data, player hand data, a number ofopponents, turn order data, a pre-flop hand strength table, and a set oftells; calculating a player weighted average equity (WAE) against eachopponent's estimated hand range based on the player hand data and thepre-flop hand strength table; determining if the player is a pre-flopraiser based on the turn order data; determining if the opponent isfirst to act and bets based on the turn order data if the player isdetermined to be the pre-flop raiser; determining a modified player WAEbased on a set of more than three ranges of player WAE if the opponentis determined to be first to act and bets; and generating a post-flopdecision from a set of post-flop decisions based on the modified playerWAE, wherein each post-flop decision from the set of post-flop decisionshas at least one corresponding modified player WAE range and the set ofpost-flop decisions consisting a call decision, a fold decision, and araise decision, and wherein the call decision has two correspondingnon-overlapping modified player WAE ranges and the raise decision andthe fold decision have one corresponding modified player WAE range, andwherein the raise decision's corresponding range of modified player WAEis between the call decision's two non-overlapping ranges of modifiedplayer WAE; and wherein the number of opponents is one, wherein each ofthe more than three ranges of player WAE have a corresponding flopdiscount factor, and wherein at least one of the more than three rangesof player WAE has a corresponding flop discount factor that is based ona set of tells and with a value that ranges between 0 and
 1. 2. Themethod of claim 1, wherein the community card poker is Texas hold'empoker.
 3. The method of claim 1, wherein generating a decision from aset of decisions is further based on making adjustments to a strategybased on an analysis of the opponent.
 4. The method of claim 3, whereinmaking adjustments to the strategy is based on an analysis of opponentprior betting statistics and exposed cards.
 5. The method of claim 3,wherein adjustments to the strategy includes: Adjusting OpponentEstimated Hand Ranges, Raising more often against loose opponents,Calling more often against loose opponents, Folding more often againsttight opponents, Bluffing more often against tight opponents, and Valuebetting more often against loose opponents.
 6. The method of claim 1,wherein the number of ranges of player WAE in the set of more than threeranges of player WAE is four.
 7. The method of claim 1, wherein the setof four ranges of player WAE consisting a first range of player WAE thatcorresponds to a folding decision, a second range of player WAE thatcorresponds to a calling decision, a third range of player WAE thatcorresponds to a raising decision, and a fourth range of player WAE thatcorresponds to a calling decision.
 8. A non-transient computer readablemedium comprising program instructions for causing a computer to performa method of: obtaining community card poker game data, the communitycard poker game data comprising estimated opponent hand data, a numberof opponents, turn order data, and a set of tells, wherein one of thetells is a decision time threshold; calculating a player weightedaverage equity (WAE) against each opponent's estimated hand range;determining if there is no pre-flop raiser based on the turn order data;determining if the opponent is first to act and bets based on the turnorder data if no one is determined to be the pre-flop raiser;determining a modified player WAE based on a set of more than threeranges of player WAE if the opponent is determined to be first to actand bets; and generating a post-flop decision from a set of post-flopdecisions based on the modified player WAE, wherein each post-flopdecision from the set of post-flop decisions has at least onecorresponding modified player WAE range and the set of post-flopdecisions consisting a call decision, a fold decision, and a raisedecision, and wherein the call decision has two correspondingnon-overlapping modified player WAE ranges and the raise decision andfold decision have one corresponding modified player WAE range, andwherein the raise decision's corresponding range of modified player WAEis between the call decision's two non-overlapping ranges of modifiedplayer WAE; and wherein the number of opponents is one, and wherein eachof the more than three ranges of player WAE have a corresponding flopdiscount factor, and wherein at least one of the more than three rangesof player WAE has a corresponding flop discount factor that is based ona set of tells and with a value that ranges between 0 and
 1. 9. Themethod of claim 8, wherein the community card poker is Texas old′empoker.
 10. The method of claim 8, wherein generating a decision from aset of decisions is further based on making adjustments to a strategybased on an analysis of the opponent.
 11. The method of claim 10,wherein making adjustments to the strategy is based on an analysis ofopponent prior betting statistics and exposed cards.
 12. The method ofclaim 10, wherein adjustments to the strategy includes: AdjustingOpponent Estimated Hand Ranges, Raising more often against looseopponents, Calling more often against loose opponents, Folding moreoften against tight opponents, Bluffing more often against tightopponents, and Value betting more often against loose opponents.
 13. Themethod of claim 8, wherein the number of ranges in the set of more thanthree ranges of player WAE is four.
 14. The method of claim 8, whereinthe set of four ranges of modified player WAE consisting a first rangeof modified player WAE that corresponds to a folding decision, a secondrange of modified player WAE that corresponds to a calling decision, athird range of modified player WAE that corresponds to a raisingdecision, and a fourth range of modified player WAE that corresponds toa calling decision.